Question
If z1,z2 and z3 are complex numbers such that
|z1|=|z2|=|z3|=∣∣1z1+1z2+1z3∣∣=1,
then |z1+z2+z3|
|z1|=|z2|=|z3|=∣∣1z1+1z2+1z3∣∣=1,
then |z1+z2+z3|
Answer: Option A
:
A
1=∣∣1z1+1z2+1z3∣∣=∣∣∣z1∗¯z1z1+z2∗¯z2z2+z3∗¯z3z3∣∣∣
(hence, |z1|2=1=z1¯¯¯¯¯z1, etc)
⇒ |z1+z2+z3|=|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|= |z1+z2+z3|
(hence,|¯¯¯¯¯z1|=|z1|)
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:
A
1=∣∣1z1+1z2+1z3∣∣=∣∣∣z1∗¯z1z1+z2∗¯z2z2+z3∗¯z3z3∣∣∣
(hence, |z1|2=1=z1¯¯¯¯¯z1, etc)
⇒ |z1+z2+z3|=|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|= |z1+z2+z3|
(hence,|¯¯¯¯¯z1|=|z1|)
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